Structural analysis is a method of simulating the behavior of a structure under various loads and conditions. Ansys is a software that offers different types of structural analysis, such as linear static analysis, nonlinear analysis, modal analysis, and transient dynamic analysis¹.
The choice of the norm depends on the type of analysis and the objective of the simulation. A norm is a measure of the error or convergence of a solution. Some common norms used in structural analysis are:
- **L2 norm**: This norm measures the difference between the exact and approximate solutions in terms of the energy norm. It is suitable for linear static analysis and modal analysis, where the solution is smooth and continuous.
- **H1 norm**: This norm measures the difference between the exact and approximate solutions in terms of both the energy norm and the gradient norm. It is suitable for nonlinear analysis and transient dynamic analysis, where the solution may have discontinuities or singularities.
- **Infinity norm**: This norm measures the maximum difference between the exact and approximate solutions at any point in the domain. It is suitable for problems where the peak values are important, such as stress concentration or contact pressure.
If you want to learn more about structural analysis methods and boundary conditions, you can check out these resources²³.
Source:
(1) Structural Analysis in ANSYS: Guide to Choosing the Right Simulation .... https://skill-lync.com/blogs/structural-analysis-in-ansys-guide-to-choosing-the-right-simulation-method.
(2) Practical Guide Structural Boundary Conditions using OnScale - Ansys. https://www.ansys.com/content/dam/amp/2023/april/quick-request/23q1-aer/structural-boundary-conditions-onscale-getsbgonen23.pdf.
(3) Static Structural Analysis - Ansys Learning Forum. https://forum.ansys.com/forums/topic/static-structural-analysis/.
The L2 norm, H1 norm, and infinity norm are different ways of measuring the error or convergence of a solution. They are based on different mathematical concepts, such as vector spaces, inner products, and norms. Here is a brief explanation of each concept:
- A **vector space** is a set of objects that can be added together and multiplied by scalars. For example, the set of all real numbers is a vector space, as well as the set of all functions defined on a domain.
- An **inner product** is a function that takes two vectors and returns a scalar. It satisfies some properties, such as symmetry, linearity, and positive-definiteness. For example, the dot product of two vectors is an inner product, as well as the integral of the product of two functions over a domain.
- A **norm** is a function that takes a vector and returns a non-negative scalar. It satisfies some properties, such as positivity, homogeneity, and triangle inequality. For example, the length of a vector is a norm, as well as the integral of the absolute value of a function over a domain.
The L2 norm, H1 norm, and infinity norm are defined using different inner products and norms on different vector spaces.
What is the difference between L2 and H1 norms?
The difference between L2 and H1 norms is that the L2 norm only measures the difference between the approximate and exact solutions in terms of the energy norm, while the H1 norm also measures the difference in terms of the gradient norm. This means that the H1 norm is more sensitive to the changes in the slope or curvature of the solution, while the L2 norm is more sensitive to the changes in the magnitude or average of the solution. The H1 norm is usually more accurate and reliable for nonlinear or transient problems, where the solution may have sharp features or discontinuities. The L2 norm is usually more efficient and simpler for linear or modal problems, where the solution is smooth and continuous.
Which standards are most often used in structural calculations in Ansys?
Structural calculations in Ansys are based on the finite element method (FEM), which is a numerical technique for solving complex problems involving structures, fluids, heat transfer, electromagnetics, and more. FEM requires the discretization of the domain into small elements, which are connected by nodes. The quality and type of the mesh affect the accuracy and efficiency of the simulation.
There are different standards or guidelines for meshing in FEM, depending on the application, geometry, and solver. Some of the most common standards are:
- **ANSYS Meshing Guidelines**: These are general recommendations for creating a good quality mesh in Ansys Mechanical or Ansys Workbench. They include tips on how to prepare the geometry, choose the element type and size, control the mesh density and refinement, and check the mesh quality. You can find more details here¹.
- **ASME Standards**: These are specific standards for meshing in FEM for pressure vessel and piping design. They are developed by the American Society of Mechanical Engineers (ASME) and are widely used in the industry. They include rules on how to define the geometry, select the element type and order, determine the mesh size and convergence, and validate the results. You can find more details here².
- **ISO Standards**: These are international standards for meshing in FEM for various engineering applications. They are developed by the International Organization for Standardization (ISO) and are accepted by many countries. They include specifications on how to model the geometry, choose the element type and shape, control the mesh density and quality, and verify the accuracy. You can find more details here³.
Source:
(1) Structural Analysis & Simulation Software | Ansys. https://www.ansys.com/products/structures.
(2) The Fundamentals of FEA Meshing for Structural Analysis - Ansys. https://www.ansys.com/blog/fundamentals-of-fea-meshing-for-structural-analysis.
(3) Static Structural Analysis - Ansys Learning Forum. https://forum.ansys.com/forums/topic/static-structural-analysis/.
(4) Structural analysis - Wikipedia. https://en.wikipedia.org/wiki/Structural_analysis.
(5) Getty Images. https://www.gettyimages.com/detail/news-photo/in-this-photo-illustration-the-ansys-logo-seen-displayed-on-news-photo/1212478964.
How do I know if my mesh is good enough for my simulation?
The quality of the mesh is important for the accuracy and efficiency of the simulation. A good mesh should have elements that are well-shaped, well-sized, and well-distributed. A bad mesh can lead to errors, convergence issues, or unrealistic results.
There are different ways to check the mesh quality in Ansys, depending on the type of mesh and the solver. Here are some general steps that you can follow:
- First, you need to choose a suitable mesh metric that reflects the quality of the mesh for your problem. Some common mesh metrics are skewness, aspect ratio, orthogonal quality, smoothness, and Jacobian ratio. You can find more details about these metrics here¹.
- Second, you need to set a threshold or a range of acceptable values for the chosen mesh metric. This depends on the element type, the solver settings, and the desired accuracy. You can find some recommended values for different mesh metrics here².
- Third, you need to display and evaluate the mesh metric on the meshed model. You can use the Mesh tab in Ansys Workbench or Ansys Mechanical to view the mesh metric statistics and histograms. You can also use the Mesh Metric option in Ansys Fluent Meshing or Ansys CFX Mesh to visualize the mesh metric on the surface or volume elements. You can find some video tutorials on how to check the mesh quality in Ansys here³⁴⁵.
- Fourth, you need to identify and improve the areas of the mesh that have poor quality elements. You can use various mesh controls and refinement techniques to modify the element shape, size, and distribution. You can also use mesh smoothing and optimization tools to improve the overall mesh quality. You can find more tips on how to improve the mesh quality in Ansys here⁶.
Source:
(1) How to check the MESH Quality in Ansys Workbench - YouTube. https://www.youtube.com/watch?v=X1km2gg_FTA.
(2) How to Check Mesh Quality in Ansys Meshing || Skewness || Orthogonality || Lec 19. https://www.youtube.com/watch?v=gEHLgFHypOE.
(3) How to Improve Surface Mesh Quality in Ansys Fluent Meshing’s Watertight Geometry Workflow. https://www.youtube.com/watch?v=nHx09ni8YQY.
(4) 10 How to Check Mesh Quality? Good OR Bad Mesh Decision |ANSYS Meshing .... https://www.youtube.com/watch?v=C6Ujgrc13EY.
(5) Looking To Element Quality In ANSYS® Meshing(Illustrated Expression) - ML. https://mechanicalland.com/looking-to-element-quality-in-ansys-meshingillustrated-expression/.
(6) https://files.mecht.in.
(7) http://mecht.in/.
(8) https://www.instagram.com/mech_tech.90/.
(9) https://www.facebook.com/mechtechpage/.
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